Skip to main content
Springer Nature Link
Log in

A survey of robust statistics

  • Original Article
  • Published:
Statistical Methods and Applications Aims and scope Submit manuscript

An Erratum to this article was published on 08 June 2007

Abstract

We argue that robust statistics has multiple goals, which are not always aligned. Robust thinking grew out of data analysis and the realisation that empirical evidence is at times supported merely by one or a few observations. The paper examines the outgrowth from this criticism of the statistical method over the last few decades.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alqallaf F, Van Aelst S, Yohai VJ, Zamar RH (2005) A model for contamination in multivariate data. Submitted

  2. Croux C, Ruiz-Gazen A (2005) High breakdown estimators for principal components: the projection-pursuit approach revisited. J Multivariate Anal 95:206–226

    Article  MATH  Google Scholar 

  3. Hubert M, Vanden Branden K (2003) Robust methods for partial least squares regression. J Chemometrics 17:537–549

    Article  Google Scholar 

  4. Hubert M, Rousseeuw PJ, Vanden Branden K (2005) ROBPCA: a new approach to robust principal components analysis. Technometrics 47:64–79

    Article  Google Scholar 

  5. Liu RY, Parelius J, Singh K (1999) Multivariate analysis by data depth: descriptive statistics, graphics and inference. Ann Stat 27:783–840

    MATH  Google Scholar 

  6. Meer P, Mintz D, Rosenfeld A, Kim DY (1991) Robust regression methods in computer vision: a review. Int J Comput Vis 6:59–70

    Article  Google Scholar 

  7. Rousseeuw PJ, Hubert M (1999) Regression depth. J Am Stat Assoc 94:388–402

    Article  MATH  Google Scholar 

  8. Rousseeuw PJ, Ruts I, Tukey JW (1999) The bagplot: a bivariate boxplot. Am Stat 53:382–387

    Article  Google Scholar 

  9. Rousseeuw PJ, Van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41:212–223

    Article  Google Scholar 

  10. Rousseeuw PJ, Van Driessen K (2006) Computing LTS regression for large data sets. Data Mining Know Discovery 12:29–45

    Article  Google Scholar 

  11. Salibian-Barrera M, Zamar RH (2002) Bootstrapping robust estimates of regression. Ann Stat 30:556–582

    Article  MATH  Google Scholar 

  12. Salibian-Barrera M, Van Aelst S, Willems G (2005) PCA based on multivariate MM-estimators with fast and robust bootstrap. J Am Stat Assoc (to appear)

  13. Salibian-Barrera M, Yohai V (2006) A fast algorithm for S-regression estimates. J Comput Graph Stat 15:414–427

    Article  Google Scholar 

  14. Van Aelst S, Rousseeuw PJ, Hubert M, Struyf A (2002) The deepest regression method. J Multivariate Anal 81:138–166

    Article  MATH  Google Scholar 

  15. Van Aelst S, Willems G (2005) Multivariate regression S-estimators for robust estimation and inference. Stat Sinica 15:981–1001

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ecole Polytechnique fédérale de Lausanne, Lausanne, Switzerland

    Stephan Morgenthaler

  2. EPFL FSB IMA, Station 8, 1015, Lausanne, Switzerland

    Stephan Morgenthaler

Authors
  1. Stephan Morgenthaler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephan Morgenthaler.

Additional information

This research was supported in part by the Swiss National Science Foundation.

An erratum to this article can be found at http://dx.doi.org/10.1007/s10260-007-0057-5

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morgenthaler, S. A survey of robust statistics. Stat. Meth. & Appl. 15, 271–293 (2007). https://doi.org/10.1007/s10260-006-0034-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10260-006-0034-4

Keywords